Question

в треугольнике АВС угол С равен 90 , СН-высота, АВ=144, sinА= 5/6. Найдите ВН

Answer 1

$sinA=BC/AB, BC=120$

$cosA=AC/AB , cosA=sqrt{1-(sinA)^2} = sqrt{11}/6$

 

$sinA=CH/AC$

$CH=20sqrt{11}$

$BH=sqrt{120^2-(20sqrt{11})^2} = 100$

$BH = 100$

$sinA=CH/AC$

$CH=20sqrt{11}$

$BH=sqrt{120^2-(20sqrt{11})^2} = 100$

$AC=24sqrt{11}$

$sinA=CH/AC$

$CH=20sqrt{11}$

$BH=sqrt{120^2-(20sqrt{11})^2} = 100$

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